ACT Preparation / Unit 14 ACT 1331 worked example, 60 to 90 seconds
Which Law to Use
The idea
For a triangle with no right angle, choose the law in three steps. First, list what is known: sides and angles, and which faces which. Second, if an angle and its opposite side are both known, plus one more part, use the law of sines. Third, if two sides and the angle between them are known, or all three sides, use the law of cosines, then finish with the law of sines or the angle sum.
In practice
Worked example: in triangle ABC, A = 40°, B = 75°, and a = 10. Angle A and its opposite side are known, so the law of sines gives b = 10 sin 75° / sin 40°, about 15.0. Second: sides 7, 8 and 13 are known, with no angles, so the law of cosines finds the largest angle: cos C = (49 + 64 − 169)/(2 × 7 × 8) = −0.5, so C = 120°.
Where people slip
Find the largest angle first with the law of cosines; it is the one that might be obtuse, which the law of sines cannot tell apart from an acute angle with the same sine.
Your place on the trail
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